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Water requirements for sprinkler systems by pipe schedule & Hydraulic calculation

Er. Parbhakar Dwivedi
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Hydraulic calculation method is the most reliable method of calculation of water flow, number of sprinklers and pipe sizes. The pipe schedule method shall not be used for designing a new installation except where the extension of existing system is required.

Hydraulic calculations shall be prepared on form sheets that include a summary sheet, detailed work sheets and graph sheets.

These sheets help monitor the water flow through the system and allow for a quick evaluation of the system. Water flow through the system is tracked in a direction opposite to that of actual flow. The first

Water supply requirements for pipe schedule sprinkler systems

Hazard category Minimum residual pressure required kgf/cm² Acceptable flow at the base of riser (LPM) Duration of flow (Minutes)
Light 1.05 1892-2840 60
Ordinary 1.40 3217-5677 90

Evaluation begins at the hydraulically most demanding sprinkler, which many time is the furthest sprinkler from the system required ends at the point of connection to the system water supply. The furthest point is chosen because if the sprinkler system is suitable to supply specified density and pressure at this point, then it will supply the required density at all other points. The fire is not expected to take place simultaneously at all places in a building. Designing a system to protect the total area of the building will thus be a futile exercise and will not only result in a heavy water storage requirements, but also heavy pumping needs.

These forms permit the designer or other persons reviewing the plans to account for individual pipe lengths and to keep track of changes in pressure and flow that results from friction loss and elevation changes.

The hydraulic calculation sheet for a typical floor area to be protected.

Let's start to fill the columns of hydraulic calculation sheet.

The floor area of the building is 39 x 60 m. The design density of 6.1 mm/min is selected from for an area of operation of 139 m2 (Refer Para 17.6.2) in ordinary hazard curves. Though a design density of 4.5 mm/min operating over an area of 279 m2 is also acceptable for ordinary hazard occupancy, (One can assume 372 m2 maximum area of operation also depending on the type of building and the protective coverage one intends to provide).

Number of sprinklers

= Area of operation/ Area of coverage per sprinkler

= 139/12 =11.54 (say 12)

As the fractional number is not possible, it is rounded to next higher value, i.e. 12 sprinklers.

Number of sprinklers on a branch line

= 1.2 √A /L

Where, L- Spacing between sprinklers on a branch line

A = Area of operation.

The multiplication by 1.2 ensures that the area of operation takes the shape of a rectangle with the longer dimension parallel to the direction of the branch line.

Note: Under certain conditions, where sprinkler were spaced 3.96 m apart on a branch line and the branch lines were spaced 3.05 m apart and calculation resulted in 12 sprinklers, some designers would calculate 4 branch lines (4 x3.05 12.20 m) with 3 sprinklers on each branch (3 x 3.96 11.88 m).

This approach would result in a design area that was almost a perfect square. The square shape would be inadequate if four sprinklers operated on the branch line Therefore, the requirement that the area of operation take the shape of a rectangle with the length of longer side having a dimension of 1.2 squire A shall be used.

L-3.9 m (by dividing total width of room equally in 10 sprinklers so as to limit the inter sprinkler distance within limit imposed.

Number of sprinklers on a branch line

= 1.2 squire139/309 = 3.58 sprinklers = 4 sprinklers.

Hydraulic calculation sheet

Step no. Nozzle identification and location Flow in LPM pipe size mm Pipe fittings and devices Equiv pipe length m Friction loss bar per meter C = 120 Pressure summary bar Notes
1 1 BL - 1 q 25 L 3.9 0.028 Pt 0.837
Q
73.2 f pe
t 3.9 pf 0.11
2 2 77.85 32 L 3.9 0.029 pt 0.947
Q
151.05 f Pe
t 3.9 pf 0.11
3 3 q 82.9 40 L 3.9 0.03 pt 1.057
Q
235.04 f Pe
t Pe pf 0.12
4 4 q 87.43 L 6.30 0.054 pt 1.17
Q 322.50 f 4.80 Pe
t 10.95 pf 0.59
5 Common main to BL 2 q L 3.0 0.016 pt 1.79
Q 322.5 f pe
t 3.0 pf 0.048
6 BL 2 Common main to BL-3 q 326.6 L 3.0 0.0245 pt 1.84
Q 649.1 62 f pe
t 3.0 pf 0.075
7 BL 3 TO Common main q 333.45 62 L 21.00 0.053 pt 1.915
Q 982.58 f Pe
t 21.00 pf 1.116
8 Common main to pump station Q 75 L 35.7 0.0186 pt 3.03
Q 982.6 f 6.3 pe 0.45
t 42.0 pf 0.77

Though the number of sprinklers on the branch line are 5, but only 4 sprinklers of this branch will form part of assumed maximum area of operation.

The values shall be rounded to next number even if the fractional part is less than 0.5.

The operating area thus becomes 4 sprinklers on each of 3 branch lines, which provides the required total of

12 sprinklers

Inter branch line distance

= Area of coverage of one sprinkler/ Inter sprinkler distance

= 12/3.9 = 3.0 m

Coming back to hydraulic sheet, sprinkler 1 and branch line 1 (BL 1) are filled in the sheet. The flow for the first sprinkler is given by the formula.

Q = D X A = 6.1 mm/min x 12 m2 = 73.2 LPM.

Where, D = design density already selected,

A = Area of coverage per sprinkler.

The final pipe size is determined by trial and error and later modified through hydraulic analysis to determine the most ideal pipe size. In this case, 25 mm pipe has been selected.

The fitting directly connected to a sprinkler is not usually included in the calculation because it is accounted for in the sprinkler's K-factor. As a result, no values are shown under pipe fittings and devices column.

The equivalent pipe length is the total center to center distance between sprinklers, which in this case is the actual pipe length of 3.9 m. The friction loss is determined by using the Hazen-Williams formula.

P =6.05Q1.85 x 105/C1.85 x d4.87

P = Frictional resistance in bar per m of pipe.

Q = Flow in litre per minute.

C = Friction loss coefficient.

D = Actual internal dia. of pipe in mm.

This is the most common of empirical formulas used to determine relationship between flow, friction loss and available pressure.

But this is dependent on the relationship between pipe types (C-factor).

The values of C-factor for various types of pipe.

Hazen-Williams C-values

S. no. Pipe type C-values
1 Unlined cast or ductile iron 100
2 Black steel 120
3 Galvanized 120
4 Plastic 150
5 Copper tube or stainless steel 150
6 Concrete 140

Thus, p = (6.05 x73.2squir1.85 x 10 squir5)/120 squir1.85 x 25 squir4.87 =0.0282 bar / m.

By multiplying with pipe length between sprinklers, i.e. 3.9 m,

P = 0.0282 x3.9 = 0.11 bar.

The total pressure at sprinkler 1 is determined by the following formula.

Páµ¼ = (Q2/l2)

Páµ¼ = Pressure in bars

Q = Flow in LPM

K = K-factor of sprinkler.

Where K- factor of sprinkler depends upon the nominal orifice size of sprinkler. The sprinkler shall have a nominal orifice size of 10 mm, 15 mm and 20 mm lists the K-factors for various nominal orifice sizes.

K-factor Values for sprinklers

Nominal orifice size (mm) Mean value of K-factor Limiting values Minimum Limiting values Maximum
10 57 54 60
15 80 76 84
20 115 109 121

Thus, Páµ¼ = (73.2)2/ (80)2 = 0.837 bar.

Similarly, pressure at sprinkler 2 is determined by adding the pressure at sprinkler 1 plus the pressure drop caused by friction loss.

P₂ = 0.837 + 0.11 = 0.947 bar.

The flow Q from sprinkler 2 is

Q₂ = k √p=80 √0.947=77.85 LPM)

Procedure for determining the friction loss and flow

In step 8, the static pressure due to elevation of sprinkler is added.

Pₑ = 4.5 m x 0.0979 (Building height 4.5 m) = 0.44 bar. Thus, the results of step 8 will help the designer to select a pump of 982 LPM (rounded to 1000 LPM) capacity discharging at a pressure of 3.03 bar.

In addition, the friction loss up to distribution pipe is to be added. The fittings and devices equivalent lengths are totalled and friction loss is calculated.

This completes the hydraulic calculation sheet.

When additional sprinkler piping is added to an existing system, the existing piping does not have to be increased in size to compensate for the additional sprinklers, provided the new work is calculated and the calculations include that portion of the existing system that can be required to carry water to the new work.

Equivalent pipe lengths of valves and fittings.

Equivalent length of fittings and values

Equivalent length of medium grade steel pipe in m according to IS 1239 (part) (c = 120) for dia. In mm equal to

fittings and valves 50 65 80 100 150 200 250
Screwed elbow 90˚ 1.46 1.89 2.37 3.04 4.30 5.67 7.42
Welded elbow 90˚ 0.69 0.88 1.10 1.43 2.00 2.64 3.35
Screwed elbow 45˚ 0.76 1.02 1.27 1.61 2.3 3.05 3.89
All other fittings 2.91 3.81 4.75 6.1 8.61 11.34 13.85
Gate valve 0.38 0.51 0.63 0.81 1.13 1.50 1.97
Alarm valve NR valve ‒ ‒ 3.94 5.07 7.17 9.40 12.30
Butterfly valve 2.19 2.86 3.55 4.56 6.38 8.62 9.90
Globe valve 6.43 21.64 126.8 34.48 48.79 64.29 84.11

For the pipe between sprinkler 1 and 2 are followed for determining the information between sprinkler 2 and 3, 3 and 4

To determine pressure loss between sprinkler 4 and cross main.

Total length of pipe = Distance between sprinkler 4 and 5 + 2.0 m between sprinkler 5 and junction + 0.3 m for riser nipple 4+2+0.3 6.3 m.

K-factor for branch line can now be determined

K = Q/√p = 322.48/√1.8 = 240

This K-factor is used in predicting the flow in subsequent branch lines which are identical to BL 1, i.e. the K-factor for BL. 1 describes the physical characteristics of the pipe opening in the cross main for the branch line and identifies the constant relationship between the flow and the pressure at this point.

Equivalent length of fittings and valves

Equivalent length of medium grade steel pipe in m according to IS 1239 (part) (c = 120) for dia. In mm equal to

fittings and valves 25 32 40
Screwed elbow 90˚ 0.77 1.04 1.22
Welded elbow 90˚ 0.36 0.49 0.56
Screwed elbow 45˚ 0.4 0.50 0.66
All other fittings 1.54 2.13 2.44

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